If $x \dagger y = x+3y$ and $x \barwedge y = 7x-y$, find $(3 \barwedge 6) \dagger -3$.
Solution: First, find $3 \barwedge 6$ $ 3 \barwedge 6 = (7)(3)-6$ $ \hphantom{3 \barwedge 6} = 15$ Now, find $15 \dagger -3$ $ 15 \dagger -3 = 15+(3)(-3)$ $ \hphantom{15 \dagger -3} = 6$.